Optimization of Sparse Concentric Ring Arrays Based on Multiple Constraints

To lower the peak sidelobe level (PSLL) of sparse concentric ring arrays, a method with multiple design constraints that embed a function model into modified real genetic algorithm (MGA) and select the grid ring radii as optimization individual to synthesize sparse concentric ring arrays is proposed. The multiple constraints include the array aperture, the minimum element spacing, and the number of elements. The proposed method dynamically calculates the ratio of element on each ring, and it has a faster convergence rate than other algorithms. The MGA uses real number to code the optimization variable, and it reduces the complexity of coding and improves the search efficiency. Finally, the results demonstrate the accuracy and effectiveness of the algorithm.

A new method of sparse array synthesis based on quantum search algorithm is proposed. The method ensures the constraints include the number of elements, the array aperture and the minimum element spacing can still be satisfied by setting rational parameters of achimedean spiral reasonably when array elements are distributed along archimedean spiral. It turns the optimization problem of sparse plane array into the optimization of asymmetrical linear arrays, which will reduce the complexity of solving problems greatly. The quantum search algorithm (QSA) is a new global optimization methods, which is inspired by quantum mechanics theories, and has excellent global optimization performance. Nowadays, the application of QSA in sparse plane arrays synthesis is few. The method combines archimedean spiral and the QSA, make the sparse plane array produce lower peak sidelobe level (PSLL). The simulated results show that the approach is high efficiency and robust, and can apply to problem of sparse plane antenna array synthesis with the constraint of minimum element spacing and aperture.

Radiation patterns are produced from concentric ring arrays by using practical elements, such as dipoles and waveguides which is presented in this article. Ring arrays, which produces high sidelobes, create electromagnetic interference (EMI) problems. To overcome this problem, analysis and synthesis is carried out and generates the directional patterns of concentric ring arrays using practical radiators. The directivity is observed for concentric dipole ring arrays and concentric waveguide ring arrays is 72.21 dB. The comparative data is presented in the result.

Designing sparse arrays with fewer antenna elements and lower peak sidelobe level (PSLL) is critical and challenging for antenna arrays in terminal devices in Internet of Things (IoT) systems. This article presents a deep learning method based on denoising diffusion probabilistic models (DDPM) for synthesizing sparse arrays. With predefined constraints such as aperture size, number of elements, and minimum element spacing, a training dataset that enables the proposed DDPM is generated to directly learn the distribution characteristics of these sparse arrays. To simplify the network architecture, the backbone network U-Net is replaced by a multilayer perceptron (MLP). In addition, an innovative conditional generation strategy is introduced to enhance the training accuracy, categorizing the training data into diverse cross-conditional labels based on PSLL and sparse ratio. During the training process, two separate regression networks are employed to predict the sparse ratio and the PSLL, and a Pareto-optimal weighting scheme (PWS) is designed to address the trade-off between them. Examples of two planar sparse arrays and a conformal sparse array demonstrate the effectiveness of the proposed DDPM-based method, highlighting its superiority in reducing PSLL and increasing sparse ratio, reducing inference time compared with the existing methods.

For the element position synthesis of 2-dimension sparse rectangular arrays with the design constraints of the number of elements, the aperture and the minimum element spacing, an improved genetic algorithm (IGA) based on chromosome element resetting is presented in this paper. Compared with the synthesis method of thinned arrays, this new approach could exploit more degree of freedom of elements to control the characters of the sparse arrays. When the aperture, the number of elements and the minimum element spacing are fixed identical, the new approach can make the sparse plane array produce lower peak sidelobe level (PSLL). The simulated results show that the fitness function value of thinned plane arrays with 108 elements mentioned by Haupt can reduce 5.626 dB when the minimum element spacing of half wavelength was introduced into the optimization. And as well, the great efficiency and the robustness of IGA are shown in this paper

In this letter, an effective approach that aims at minimizing the peak-sidelobe level of uniform amplitude concentric ring arrays (UACRAs) is presented. The element number in each ring is specified by a new deterministic formulation derived from the continuous weighting-density approximation. Meanwhile, the ring radii are adjusted by a fine-adjustment synthesis procedure. This newly developed method is flexible to synthesize UACRAs with multiple constraints, such as total number of array elements, aperture size, and minimum element spacing. Some examples are provided to demonstrate the outperformance of this approach.

A novel method is presented to design beam-scannable ultra-wideband (UWB) sparse arrays. A concept of design frequency is introduced which transforms the beam-scannable UWB array design to the problem of synthesizing a broadside-beam array at single frequency. The raised power series (RPS) representation with appropriate parameter selection is adopted to generate initial element positions, and then an iterative convex optimization is applied to successively optimize the element positions for further sidelobe level (SLL) reduction. Multiple constraints for controlling the first-order Taylor expansion accuracy, the minimum element spacing, and the array aperture are incorporated in the iterative convex optimization to obtain stable and practical synthesis results. Several examples for synthesizing UWB arrays with different frequency bands, beam scanning, ranges and element counts are conducted to validate the effectiveness and advantages of the proposed method. It is shown that the proposed method achieves much lower SLLs than those by the original RPS method for all test cases, and it also significantly outperforms some conventional stochastic optimization methods for large UWB array cases.

Beampattern of a frequency diverse array (FDA) is a function of time, range and angle. The shape of this beampattern is dependent on the frequency offsets (FO) that are applied to each element. These FO are sampled from a window function whose parameters are optimised to yield minimum peak side lobe level (PSLL) and half‐power beamwidth (HPBW). Time‐variance is usually ignored because it can be removed by signal processing at the receiver. However, the travelling beam is still time‐variant. This work shows that, in a time‐variant beampattern, the optimum PSLL of these window functions degrade while HPBW is unaffected. A window function that is based on a sum of three Sinc functions (s‐Sinc) is proposed for FO optimisation. The superiority of this window is established by comparing the optimum PSLL and HPBW in a time‐invariant scenario. Later, time‐variance is introduced, and s‐Sinc function is used to minimise time‐variant PSLL and HPBW. Results show that a beampattern with low time‐variant PSLL and HPBW can be synthesised compared to their time‐invariant counterparts.

A hybrid algorithm based on the invasive weed optimization (IWO) and the convex optimization (CVX) is proposed for minimizing the peak sidelobe level (PSLL) of linear array with focused and/or shaped beam pattern. In this approach, IWO is adopted to produce the array (described by element positions), and CVX is used to determine the excitations for each produced array. Then the corresponding PSLL acts as the fitness function of IWO to find the optimal positions which lead to the minimum PSLL. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed hybrid approach. Compared with other techniques, a lower PSLL can be achieved with a fixed main beam width or with a shaped main beam using this hybrid algorithm. Moreover, this method can easily cope with some constraints on the aperture, such as the minimum element spacing and the total number of elements.

Controlling peak side-lobe level (PSL) is of great importance in\nhigh-resolution applications of multiple-input multiple-output (MIMO) radars.\nIn this paper, designing sequences with good autocorrelation properties are\nstudied. The PSL of the autocorrelation is regarded as the main merit and is\noptimized through newly introduced cyclic algorithms, namely; PSL Minimization\nQuadratic Approach (PMQA), PSL Minimization Algorithm, the smallest Rectangular\n(PMAR), and PSL Optimization Cyclic Algorithm (POCA). It is revealed that\nminimizing PSL results in better sequences in terms of autocorrelation\nside-lobes when compared with traditional integrated side-lobe level (ISL)\nminimization. In order to improve the performance of these algorithms,\nfast-randomized Singular Value Decomposition (SVD) is utilized. To achieve\nwaveform design for MIMO radars, this algorithm is applied to the waveform\ngenerated from a modified Bernoulli chaotic system. The numerical experiments\nconfirm the superiority of the newly developed algorithms compared to\nhigh-performance algorithms in mono-static and MIMO radars.\n

This paper presents a kind of particle swarm optimization (PSO) algorithm which is based on simulated annealing (SA) for the synthesis of sparse linear arrays. This algorithm is used to optimize the element positions to suppress the peak side lobe level (PSLL) of the array with many constraints. With this method the freedom increase amounts are used as optimization variables, which plus the minimum element spacing constraint is deemed as element spacing of the array. And the method has downsized the searching region by indirect expression of element spacing. The simulated optimization results demonstrate the better suppression effect of PSLL of the proposed algorithm.

A hybrid method is proposed for synthesizing sparse concentric ring arrays (CRAs) to get circularly symmetric and invariant three-dimensional (3-D) patterns over all-azimuth directions. The hybrid method involves a convex optimization approach and a determined approach together. Based on the Bessel function approximation of the circular array pattern and the compressed sensing (CS) theory, the synthesis of a sparse concentric current ring array can be formulated as a convex problem with the minimization of l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm, and the corresponding array parameters including the number of concentric rings, the ring radii, and the current ring excitations can be determined simultaneously to satisfy the requirements on radiation pattern. In order to reconstruct the 3-D pattern accurately with discrete antenna elements in place of the current rings, a determined approach with or without radial amplitude weighting is proposed to define the number of elements equally distributed on each ring. The proposed hybrid method can be applied to synthesizing CRAs with 3-D pattern either matching a desired pattern or satisfying a prescribed power mask. Moreover, the method is very easy to implement, while has good numerical stability and computational efficiency. Numerical experiments are conducted to validate the flexibility and effectiveness of the proposed method.

This paper addresses a novel rotationally symmetric technique with multiple constraints for sparse conformal array synthesis. The purpose is to synthesis a sparse optimal common element positions on the conformal surface varying multiple patterns of wide angle scanning with the behavior of low sidelobe levels (SLL). The conformal surface aperture is partitioned into several rotationally symmetric sections. The element positions and element numbers of only one section need to be optimized, which contribute to the reduction of optimizing variables and computation resources. We formulate the synthesis problem as a constrained optimization problem, which takes the peak sidelobe level (PSLL) as the fitness function, and sets the total number of array elements, the minimum spacing between two adjacent elements to form multiple constraints. The Brain Storm Optimization (BSO) is further exploited into the synthesis problem with multiple constraints. A set of representative numerical examples are presented to assess the advantages and effectiveness of the proposed method.

A multiobjective approach based on the third evolution step of generalized differential evolution (GDE3) algorithm is proposed for optimizing the time-modulated array (TMA) in this paper. Different from the single-objective optimization, which optimizes a weighted sum of the peak sidelobe level (PSLL) and the peak sideband level (PSBL) of the array, the multiobjective algorithm treats the PSLL and the PSBL as two distinct objectives that are to be optimized simultaneously. Furthermore, not only one outstanding optimization result can be acquired but also a set of solutions known as Pareto front is obtained by using the GDE3 algorithm, which will guide the design of time-modulated array more effectively. Users can choose one appropriate outcome which has a suitable tradeoff between the PSLL and the PSBL. This approach is illustrated through a time-modulated concentric circular ring array (CCRA). The optimal parameters and the corresponding radiation patterns are presented at last. Experimental results reveal that the multiobjective optimization can be an effective approach for the TMA synthesis problems.

Among phase continuously and randomly coded waveforms it is shown that the quadriphase-coded (QPC) waveform has the best peak-to-sidelobe ratio (PSR). Hence a QPC waveform coded by a binary sequence with the minimum peak sidelobe level (PSL) results in a continuous phase modulated (CPM) waveform with the optimal PSR. To improve the spectrum of the original QPC waveform, the Gaussian minimum shift keying (GMSK) coding function is used to code the QPC waveform making the phase continuous and differentiable. In addition, a spectral optimisation model is proposed to further refine the GMSK-coded QPC waveform. The final product is a constrained-bandwidth constant-amplitude waveform whose phase profile is continuous, smooth and differentiable. It has optimal PSR and optimal spectrum which quite satisfies the criteria specified by the US National Telecommunications and Information Administration (NTIA).